Method and device for determining a driving signal for vibroseis marine sources

ABSTRACT

Controller and method for determining a driving signal of a vibro-acoustic source element that is configured to generate acoustic waves in water. The method includes estimating at least one physical constraint of the vibro-acoustic source element; modeling a ghost function determined by a surface of the water; setting a target energy spectrum density to be emitted by the vibro-acoustic source element during the driving signal; and determining the driving signal in a controller based on at least one physical constraint, the ghost function, and the target energy spectrum density.

BACKGROUND

1. Technical Field

Embodiments of the subject matter disclosed herein generally relate tomethods and systems and, more particularly, to mechanisms and techniquesfor generating a driving signal for vibroseis marine sources.

2. Discussion of the Background

Reflection seismology is a method of geophysical exploration todetermine the properties of a portion of a subsurface layer in theearth, which is information especially helpful in the oil and gasindustry. Marine reflection seismology is based on the use of acontrolled source that sends energy waves into the earth. By measuringthe time it takes for the reflections to come back to plural receivers,it is possible to estimate the depth and/or composition of the featurescausing such reflections. These features may be associated withsubterranean hydrocarbon deposits.

For marine applications, sources are essentially impulsive (e.g.,compressed air is suddenly allowed to expand). One of the most usedsources is airguns. An airgun produces a high amount of acoustics energyover a short time. Such a source is towed by a vessel either at thewater surface or at a certain depth. The acoustic waves from the airgunpropagate in all directions. A typical frequency range of the emittedacoustic waves is between 6 and 300 Hz. However, the frequency contentof impulsive sources is not fully controllable, and different sourcesare selected depending on the needs of a particular survey. In addition,the use of impulsive sources can pose certain safety and environmentalconcerns.

Thus, another class of sources that may be used is vibratory sources.Vibratory sources, including hydraulically powered sources and sourcesemploying piezoelectric or magnetostrictive material, have been used inmarine operations. However, there is no large-scale use of such sourcesbecause they have limited power and are not reliable due to the numberof moving parts required to generate the seismic waves. A few examplesof such sources are now discussed.

A marine vibrator generates a long tone with a varying frequency, i.e.,a frequency sweep. This signal is applied to a moving part, e.g., apiston, which generates a corresponding seismic wave. Instantaneouspressure resulting from the movement of plural pistons corresponding toplural marine vibrators may be lower than that of an airgun array, buttotal acoustic energy transmitted by the marine vibrator may be similarto the energy of the airgun array due to the extended duration of thesignal. However, such sources need a frequency sweep to achieve therequired energy. Designing such a frequency sweep is now discussed.

U.S. Patent Application Publication No. 20100118647A1, entitled, “Methodfor optimizing energy output from a seismic vibrator array,” the entiredisclosure of which is incorporated herein by reference, discloses twoflextensional vibrators (low frequency and high frequency) activated byelectro-mechanical actuators and emitting seismic energy at twodifferent depths during a frequency sweep. The vibrators are driven byswept frequency signals, each having a different selected frequencyresponse. Signals such as Maximum Length Sequence (MLS) or Gold Sequence(GS) are also used to drive the vibrators. However, the driving signalof this document does not take into account various physical constraintsof the seismic vibrator or the medium in which the vibrator operates.

A non-linear frequency sweep is described in U.S. Pat. No. 6,942,059B2,entitled, “Composite bandwidth marine vibroseis array,” the entirecontent of which is incorporated herein by reference. This documentdiscloses a method for seismic marine survey using vibrator sources,each of them placed at different depths. The vibrator sources show alevel of seismic energy comparable to an airgun array (single depth) bydividing the seismic bandwidth over a plurality of different bandwidths.Each bandwidth is generated by a vibrator array using a non-linear sweepin order to maximize the output energy. However, this document does notconsider the various physical constraints of the marine vibroseis arraywhen determining the frequency sweep.

A sweep design method for a seismic land vibrator is also disclosed inU.S. Pat. No. 7,327,633, entitled, “Systems and methods for enhancinglow-frequency content in vibroseis acquisition,” the entire content ofwhich is incorporated herein. The patent discloses a method foroptimizing sweep signal strength by taking into account a singlephysical property of a seismic land vibrator, i.e., a stroke limit ofthe seismic vibrator device. A non-linear sweep is obtained in order tobuild up the sweep spectral density to achieve a targeted spectrum inthe low frequency range. However, other physical properties of theseismic land vibrator, which limit the operation of the land vibrator,are not considered. Further, this patent is directed to a land vibrator,which is different from a marine vibrator.

A more sophisticated sweep design method is disclosed in U.S. patentapplication Ser. No. 12/576,804, entitled, “System and method fordetermining a frequency sweep for seismic analysis,” the entire contentof which is incorporated herein by reference. This method takes intoaccount not only the plate stroke limit but also other constraints ofthe land vibrator, e.g., the pump flow limit and the servo valve flowlimit. However, this method addresses a land vibrator, which hasdifferent characteristics than a marine vibrator, and the method alsodoes not take into consideration specific features of the waterenvironment.

Thus, there is a need to provide a method for designing a driving signalthat takes into account constraints of the marine vibrator and,optionally, constraints imposed by the water environment.

SUMMARY

According to one exemplary embodiment, there is a method for determininga driving signal of a vibro-acoustic source element that is configuredto generate acoustic waves in water. The method includes a step ofestimating at least one physical constraint of the vibro-acoustic sourceelement; a step of modeling a ghost function determined by a surface ofthe water; a step of setting a target energy spectrum density to beemitted by the vibro-acoustic source element during the driving signal;and a step of determining the driving signal in a controller based onthe at least one physical constraint, the ghost function, and the targetenergy spectrum density.

According to still another exemplary embodiment, there is a controllerconfigured to determine a driving signal of a vibro-acoustic sourceelement that is configured to generate acoustic waves in water. Thecontroller includes a processor configured to, estimate at least onephysical constraint of the vibro-acoustic source element; receive aghost function determined by a surface of the water; receive a targetenergy spectrum density to be emitted by the vibro-acoustic sourceelement during the driving signal; and calculate the driving signalbased on the at least one physical constraint, the ghost function, andthe target energy spectrum density.

According to still another exemplary embodiment, there is a seismicsurvey system that includes at least one vibro-acoustic source elementconfigured to generate acoustic waves by moving a piston with anelectro-magnetic actuator; a driving mechanism connected to theelectro-magnetic actuator and configured to drive the electro-magneticactuator to generate the acoustic waves; and a controller configured togenerate a driving signal for the driving mechanism for generatingacoustic waves in water. The controller is configured to estimate atleast one physical constraint of the vibro-acoustic source element;receive a ghost function determined by a surface of the water; receive atarget energy spectrum density to be emitted by the vibro-acousticsource element during the driving signal; and calculate the drivingsignal based on the at least one physical constraint, the ghostfunction, and the target energy spectrum density.

According to yet another exemplary embodiment, there is a computerreadable medium including computer executable instructions, wherein theinstructions, when executed, implement the above-noted method.

According to still another exemplary embodiment, there is a method fordetermining a driving signal of a vibro-acoustic source element that isconfigured to generate acoustic waves in water. The method includes astep of estimating at least one physical constraint of thevibro-acoustic source element; a step of setting a target energyspectrum density to be emitted by the vibro-acoustic source elementduring the driving signal; and a step of determining the driving signalin a controller based on the at least one physical constraint, and thetarget energy spectrum density.

According to a further exemplary embodiment, there is a seismic surveysystem that includes at least one vibro-acoustic source elementconfigured to generate acoustic waves by moving a piston with anactuator; a driving mechanism connected to the actuator and configuredto drive the actuator to generate the acoustic waves; and a controllerconfigured to generate a driving signal for the driving mechanism forgenerating the acoustic waves in water. The controller is configured toestimate at least one physical constraint of the vibro-acoustic sourceelement; receive a target energy spectrum density to be emitted by thevibro-acoustic source element during the driving signal; and calculatethe driving signal based on the at least one physical constraint, andthe target energy spectrum density.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate one or more embodiments and,together with the description, explain these embodiments. In thedrawings:

FIG. 1 is a schematic diagram of a vibro-acoustic source element;

FIG. 2 is a schematic diagram of a driving mechanism for avibro-acoustic source element;

FIG. 3 is an electro-mechanical model for a vibro-acoustic sourceelement according to an exemplary embodiment;

FIG. 4 is a graph showing a maximum acceleration of a vibro-acousticsource element as a function of various parameters according to anexemplary embodiment;

FIG. 5 is a graph illustrating a maximum far field sound pressure levelof a vibro-acoustic source element as a function of frequency accordingto an exemplary embodiment;

FIG. 6 is a schematic representation of a vibro-acoustic source elementaccording to an exemplary embodiment;

FIG. 7 is a target output energy density spectrum according to anexemplary embodiment;

FIGS. 8 a and 8 b illustrate a vertical ghost function for two differentdepths;

FIGS. 9 a and 9 b illustrate a ghost function for two differentelevation angles;

FIG. 10 is a schematic representation of a method for determining adriving signal for a vibro-acoustic source element according to anexemplary embodiment;

FIG. 11 is a schematic representation of a driving signal according toan exemplary embodiment;

FIG. 12 is a schematic representation of a free far field sound pressuregenerated by a vibro-acoustic source element according to an exemplaryembodiment;

FIG. 13 is a schematic representation of a far field sound pressuregenerated by a vibro-acoustic source element and a corresponding ghostaccording to an exemplary embodiment;

FIG. 14 is a flow chart of a method for generating a driving signal fora vibro-acoustic source element according to an exemplary embodiment;

FIG. 15 is a flow chart of another method for generating a drivingsignal for a vibro-acoustic source element according to an exemplaryembodiment; and

FIG. 16 is a schematic diagram of a controller according to an exemplaryembodiment.

DETAILED DESCRIPTION

The following description of the exemplary embodiments refers to theaccompanying drawings. The same reference numbers in different drawingsidentify the same or similar elements. The following detaileddescription does not limit the invention. Instead, the scope of theinvention is defined by the appended claims. The following embodimentsare discussed, for simplicity, with regard to a method to generate ordesign a driving signal for a vibro-acoustic source element and/or amarine source array for achieving a desired target output spectrum incompliance with various constraints of each vibro-acoustic sourceelement and other constraints such as environmental constraintsintroduced by the marine seismic acquisition. However, the embodimentsto be discussed next are not limited to a marine seismic source, but maybe applied to other structures that generate a seismic wave having acontrolled frequency range.

Reference throughout the specification to “one embodiment” or “anembodiment” means that a particular feature, structure, orcharacteristic described in connection with an embodiment is included inat least one embodiment of the subject matter disclosed. Thus, theappearance of the phrases “in one embodiment” or “in an embodiment” invarious places throughout the specification is not necessarily referringto the same embodiment. Further, the particular features, structures, orcharacteristics may be combined in any suitable manner in one or moreembodiments.

According to an exemplary embodiment, there is a method for determininga driving signal, for a vibro-acoustic source element or a marine sourcearray, which takes into account various constraints of the source. Forexample, if the vibro-acoustic source element has an electro-magneticactuator that is driven by a driving mechanism that includes anamplifier, the method identifies physical properties of both theactuator and the amplifier that may limit the ability of thevibro-acoustic source element to provide the expected output, such asthe source element stroke limit (e.g., actuator stroke limit), thesource element velocity limit, the amplifier current limit, and theamplifier voltage limit. Identification of an additional environmentalconstraint introduced by the sea surface reflector, known as the “ghostfunction,” is also taken into account by this novel method. The methoddetermines a driving signal that may be modulated both in frequency andamplitude. The driving signal is configured to achieve a target outputspectrum with maximum energy output while complying with multipleconstraints. Various target output spectrums may be considered. However,for simplicity, the following embodiments discuss a flat target outputspectrum.

It is noted that the method discussed below considers a vibro-acousticsource element that is driven by a driving mechanism. However, themethod may be applied to other vibratory sources.

Prior to discussing the above-noted method, an exemplary vibro-acousticsource element is now discussed with reference to FIG. 1. According toan exemplary embodiment, the vibro-acoustic source element 10 of FIG. 1is part of a seismic source array. The vibro-acoustic source element 10includes an enclosure 20 that together with pistons 30 and 32 enclose anelectro-magnetic actuator system 40 and separate it from the ambient 50,which might be water. The enclosure 20 has first and second openings 22and 24 that are configured to be closed by the pistons 30 and 32. Theelectro-magnetic actuator system 40 is configured to simultaneouslydrive the pistons 30 and 32 in opposite directions for generating theseismic waves. In one application, the pistons 30 and 32 are rigid. Theelectro-magnetic actuator system 40 may include two or more individualelectro-magnetic actuators 42 and 44. Irrespective of how manyindividual electro-magnetic actuators are used in the vibro-acousticsource element 10, the actuators may be provided in pairs, and the pairsare configured to act simultaneously in opposite directions oncorresponding pistons in order to prevent a “rocking” motion of thevibro-acoustic source element 10. However, the method also applies to avibro-acoustic source element that has only one actuator and one piston.

The size and configuration of the electro-magnetic actuators depend onthe acoustic output of the vibro-acoustic source element. FIG. 1 showsthat the two actuators 42 and 44 are separated by a wall 46, which doesnot have to be at the middle of the actuator system 40. Further, in oneembodiment, the two actuators 42 and 44 are formed as a single unit, andthere is no interface between the two actuators. In yet anotherapplication, the actuator system 40 is attached to the enclosure 20 byan attachment 48. The attachment 48 may be a strut-type structure. Inone application, the attachment 48 may be a wall that splits theenclosure 20 in a first chamber 20 a and a second chamber 20 b. If theattachment 48 is a wall, the actuators 42 and 44 may be attached to thewall 48 or may be attached to the enclosure 20 by other means in such away that the actuators 42 and 44 do not contact the wall 48.

To provide the pistons 30 and 32 with the ability to move relative tothe enclosure 20 in order to generate the seismic waves, a sealingmechanism 60 is provided between the pistons and the enclosure. Thesealing mechanism 60 may be configured to slide back and forth with thepistons. The sealing mechanism 60 may be made of an elastomericmaterial, or may be a metallic flexible structure. In anotherapplication, the sealing mechanism 60 may be a gas or liquid seal. A gasseal (air bearing seal) is configured to inject a gas at the interfacebetween the enclosure and the pistons to prevent the ambient water fromentering the enclosure. A liquid seal may use, e.g., a ferromagneticfluid at the interface between the enclosure and the pistons to preventthe ambient water from entering the enclosure. Other seals may be usedas will be recognized by those skilled in the art.

The embodiment shown in FIG. 1 may also include a pressure regulationmechanism 70 (e.g., a pneumatic regulation mechanism if air is used).The pressure regulation mechanism 70 may be used to balance the externalpressure of the ambient 50 with a pressure of the medium enclosed by theenclosure 20 to reduce the workload of the actuator system 40. It isnoted that if pressure of the ambient at point 72 (in front of thepiston 30) is substantially equal to pressure of the enclosed medium 73of the enclosure 20 at point 74, the workload of the actuator system 40may be used entirely to activate the piston to generate the acousticwave instead of a portion thereof used to overcome the ambient pressureat point 72. The enclosed medium 73 of the enclosure 20 may be air orother gases or mixtures of gases.

The pressure regulation mechanism 70 may be fluidly connected to apressure source (not shown) on the vessel towing the vibro-acousticsource element 10. The pressure regulation mechanism 70 may also beconfigured to provide an additional force on the pistons 30 and 32,e.g., at lower frequencies, to increase an acoustic output of thevibro-acoustic source element and also to extend a frequency spectrum ofthe vibro-acoustic source element.

The embodiment illustrated in FIG. 1 may use a single shaft 80 and 82per piston to transmit the actuation motion from the actuator system 40to the pistons 30 and 32. However, more than one shaft per piston may beused, depending on the requirements of the vibro-acoustic sourceelement. To provide a smooth motion of the shaft 80 relative to theenclosure 20 (e.g., to prevent a wobbling motion of the shaft), aguiding system 90 may be provided.

In one application, heat is generated by the actuator system 40. Thisheat may affect the motion of the shafts and/or the functioning of theactuator system 40. For this reason, a cooling system 94 may be providedat the vibro-acoustic source element. The cooling system 94, as will bediscussed later, may be configured to transfer heat from the actuatorsystem 40 to the ambient 50.

The pistons 30 and 32 are desired to generate an output having apredetermined frequency spectrum. To control this output, a localcontrol system 200 may be provided, inside, outside, or both, relativeto the enclosure 20. The local control system 200 may be configured toact in real-time to correct the output of the vibro-acoustic sourceelement 10. As such, the local control system 200 may include one ormore processors that are connected to sensors that monitor the status ofthe vibro-acoustic source element 10 and provide commands for theactuator system 40 and/or the pressure regulation mechanism 70.

The source arrays discussed above may be made up entirely of thevibro-acoustic source element illustrated in FIG. 1. However, the sourcearrays may be made up of different vibroseis source elements or acombination of those shown in FIG. 1 and those known in the art.Depending on the vibro-acoustic source element, the method determinesdifferent driving signals because the driving signal is dependent on thespecific construction and characteristics of the consideredvibro-acoustic source element. A driving signal may be a frequency sweepas known in the art, i.e., a signal that includes plural frequenciesthat are produced one at a time in a certain temporal order. However,the driving signal is not limited to the frequency sweep but may includea non-continuous signal, a signal that includes plural frequenciesemitted at the same time, etc.

For a better understanding of the constraints imposed on thevibro-acoustic source element by its associated driving mechanism, FIG.2 illustrates a generic arrangement for the driving mechanism. Such adriving mechanism 250 is electrically connected to the vibro-acousticsource element 10 and is configured to apply a driving signal to drivethe electro-mechanical actuator of the vibro-acoustic source element 10.An exemplary structure of the driving mechanism 250 may include aprocessor 252 for generating the driving signal. For example, in oneapplication, the processor 252 has a first component that is configuredto generate a baseband carrier signal. The baseband carrier signal mayhave characteristics as known to those skilled in the art. A secondcomponent of the processor 252 may act as a pseudo-random number signalgenerator, and may be configured to generate a signal that is mixed in athird component with the signal of the first component. The mixed signalmay be amplified by a fourth component prior to being provided to thevibro-acoustic source element 10. It is noted that the driving mechanism250 may be part of the vibro-acoustic source element 10 or may beprovided outside the vibro-acoustic source element. Also, it is notedthat other configurations for the driving mechanism 250 may be used asthose skilled in the art would recognize.

With this structure of the driving mechanism 250 and the structure ofthe vibro-acoustic source element 10 discussed with regard to FIG. 1, aschematic representation of some characteristics of the drivingmechanism and the vibro-acoustic source element are shown in FIG. 3.Again, it is noted that other vibro-acoustic source elements or otherdriving mechanisms may be used. FIG. 3 illustrates a lumped elementmodel for the electrical and mechanical components of the vibro-acousticsource element 10 and also for the electrical components of a componentof the driving mechanism 250 that acts as an electrical amplifier. Morespecifically, the model 300 shown in FIG. 3 has an electrical part 302that corresponds to the electro-magnetic actuator and the drivingmechanism of the vibro-acoustic source element, and a mechanical part304 that corresponds to the piston of the vibro-acoustic source element.

The electrical part 302 includes a current source 310 represented by I₀,a coil resistance 312 represented by R_(e), and a coil inductance 314represented by L_(e), where the coil is part of the electro-magneticactuator discussed above with regard to FIG. 1. An induced electromotivevoltage 316 represented by U appears into the coil, and this voltage isresponsible for actuating the piston of the electro-magnetic actuator.The mechanical part 304 includes the piston mass and acoustic reactance320 represented by M_(t), a total mechanical stiffness 322 representedby C_(t), and a mechanical damping and acoustic radiation 324represented by R_(mt). Through a coupling 330 between the electricalpart 302 and the mechanical part 304, a Lorentz force 332 produced bythe electrical part is transmitted to the mechanical part, where theLorentz force is proportional to the current of the current source 310.

With this model for the vibro-acoustic source element, it is nowpossible to determine the influence of various physical constraints onthe seismic output. A good quantity for estimating the seismic output ofthe vibro-acoustic source element is the acceleration of the piston. Theacceleration of the piston (and also a far field sound pressure that isrelated to the acceleration, as will be discussed later) is limited forthe representation considered in FIG. 3 by at least four factors. Thesefactors are the maximum displacement of the piston X_(max), the maximumspeed of the piston V_(max), the maximum current I_(max) that may begenerated by the driving mechanism shown in FIG. 2, and the maximumvoltage U_(max) of the same device. The maximum acceleration of thepiston is determined, for example, for each of these four factors byequations:

a_(max) = −ω²X_(max), a_(max) = ωV_(max), a_(max) = jω BlG_(m)I_(max), and$a_{\max} = {\frac{{j\omega}\; {BlG}_{m}U_{\max}}{Z_{in}}.}$

The quantities G_(m) and Z_(in) depend on the parameters shown in FIG.3.

The maximum acceleration a_(max) may be plotted on the same graph, asshown in FIG. 4, for the four factors. Thus, curve 340 corresponds toX_(max), curve 342 corresponds to V_(max), curve 344 corresponds toI_(max) and curve 346 corresponds to U_(max). The intersection of thesecurves corresponding to the four factors determines an area 350 that isrepresentative of an available operating range of the vibro-acousticsource element. This means that as long as the vibro-acoustic sourceelement operates in the area 350 defined by these factors, a sustainableoutput of the vibro-acoustic source element is expected.

As the maximum acceleration of the piston is related to the maximumsound pressure in a far field in a free-field, the maximum soundpressure has the shape shown in FIG. 5. FIG. 5 illustrates a soundpressure in dB at 1 m from the source with a reference of 1 μPa. It isnoted that the values shown on the Y axis in both FIGS. 4 and 5 arescaled. For example, the maximum sound pressure may be related to themaximum acceleration by the relation:

${{p_{\max}\left( {r,{j\omega}} \right)} = {\frac{\rho}{4\pi \; r}{{Sa}_{\max}({j\omega})}}},$

where ρ is the density of the medium and S is the area of the piston.Regarding the area S, it is noted that for the specific vibro-acousticsource element discussed with regard to FIG. 1, there are two pistons.In this regard, FIG. 6 schematically shows the vibro-acoustic sourceelement 10 having a first projector 402 and a second projector 404, thetwo projectors arranged back-to-back. Each projector has its own piston402 a and 404 a. As the projectors are actuated in phase and areback-to-back, the vibro-acoustic source element 10 acts as a monopole,i.e., a point source. With this clarification, it is noted that area Sin the above formula includes the area of two pistons 402 a and 404 a.Of course, for other configurations, for example, a vibro-acousticsource element with only one projector, or more than two projectors, oranother type of vibro-acoustic source element, the area S and the aboveequation need to be adjusted accordingly.

Up to this point, the physical constraints of the vibro-acoustic sourceelement have been discussed and are specific for the vibro-acousticsource element shown in FIG. 1. For other types of source elements,other constraints may be considered. Based on the teachings of the aboveembodiments, one skilled in the art would know how to determine thephysical constraints for the source at hand. Next, a target shape for anenergy spectral density is discussed, still with regard to thevibro-acoustic source element shown in FIG. 1.

For determining the energy that should be provided by the drivingsignal, the sound pressure level discussed above does not provide enoughinformation. The quantity that provides the missing information is theenergy spectral density (ESD). The ESD for a finite energy signal (e.g.,a sweep) in dB at 1 m in μPa/Hz is given by:

${{ESD}_{d\; B} - {10\log_{10}\frac{{ESD}(f)}{\left( 10^{- 6} \right)^{2}}}},$

where ESD(f) is the energy spectral density at 1 m from the source inPa²/Hz and is given by a Fast Fourier Transform of the pressure. Fromhere, using, for example, a Parseval operation, the acoustic energy ofthe source can be calculated.

For the given vibro-acoustic source element, it is desired to determinethe driving signal such that a target ESD is obtained. There are variouspossible shapes for the desired ESD depending on the nature of thesurvey, the intended features to be revealed, etc. As an example, FIG. 7shows a flat ESD over 4 to 128 Hz. A flat ESD has the advantage thatincreases the resolution of the final image for most of the frequenciesin the frequency band. Thus, the ESD shown in FIG. 7 is the ESD targetshape. However, it is noted that the ESD may have other shapes, forexample, a sinus shape or other non-regular shapes.

Another constraint for calculating the driving signal is now discussedin more detail. This constraint, which is due to the environment, is the“ghost function.” By taking into account this constraint, a final imageof the subsurface to be obtained with this source is better. However, itis noted that the ghost function may be ignored when determining thedriving signal for the vibro-acoustic source element. The ghost functionmay be seen as a weighting function applied to the energy spectrumdensity. Because a single vibro-acoustic source element or a seismicsource array (including plural vibro-acoustic source elements) may beused at a specific depth, certain notches appear in the amplitudespectrum within the seismic frequency range, depending on the depth.These notches are caused by the sea surface reflected waves interferingwith direct arrival waves (the constructive and destructive interferenceof these waves creating the ghost effect). Therefore, the ghost functionmay be considered when designing the driving signal.

According to an exemplary embodiment, the ghost function may take theform g(d,θ)=2 sin(kd·cos θ), where d is a depth of the vibro-acousticsource element relative to the sea surface, k is wavenumber, and θ is anelevation angle (elevation angle describes the position of an observerrelative to a vertical line through the vibro-acoustic source element).An example of the ghost function for two different depths at zeroelevation angle is shown in FIG. 8 a, with curve 800 illustrating theghost function for a first depth and curve 802 corresponding to a seconddepth, smaller than the first depth. FIG. 8 b illustrates the twopositions 804 and 806 of the sources relative to the sea surface 808having the elevation angle zero. FIG. 9 a shows the dependence of theghost function with the frequency for various elevation angles for agiven depth. Curve 900 illustrates this dependence for a zero elevationangle, and curve 902 illustrates the dependence for a 60° elevationangle. FIG. 9 b shows the two elevation angles relative to the source904.

In both FIGS. 8 a and 9 a it is noted that the ghost function introducesnotches at various frequencies and also boosts the spectrum at otherfrequencies. Thus, a careful consideration of the ghost function whendetermining the ESD target helps improve the ESD in the low-frequencyrange, which is advantageous as the low-frequency range of the spectrumoffers a better resolution of the subsurface at deeper levels.

Having now all the ingredients necessary for designing the drivingsignal, i.e., the physical constraints of the vibro-acoustic sourceelement, the target ESD, and, optionally, the ghost function, afrequency-dependent far-field sound pressure P that can be generatedwithout exceeding the vibro-acoustic source element specifications canbe determined. Considering this acoustic pressure to be P and theinstantaneous frequency to be f_(i)(t), a maximum far-field soundpressure in free-field can be written as:

P(t)=P _(max)(f _(i)(t))·sin(2π∫₀ ^(t) f _(i)(t)dt+φ),

where φ is the sweep initial time. The free-field condition assumes thatthe waves emitted by the vibro-acoustic source element are not reflectedat the water-air interface or that there is no water-air interface.Thus, the free-field condition is free of ghosts. The instantaneousfrequency can be determined by inverting the instantaneous time asfollows:

${{t_{i}(f)} = {\int_{f_{\min}}^{f_{\max}}{4\frac{{ESD}(f)}{P^{2}(f)}\ {f}}}},$

where ESD(f) is the desired far-field energy spectrum density infree-field, but taking into account the ghost weighting function, andf_(min) and f_(max) are the sweep minimum and maximum frequencies,respectively. Based on this instantaneous frequency law, the drivingsignal is generated according to maximum available amplitude thatpermits the transmission of the far-field signature with maximum energy.The instantaneous frequency law is illustrated in FIG. 10. A controldevice 1000 (to be discussed later) is configured to take as input thephysical constraints 1010 of the vibro-acoustic source element, the ESDtarget 1020, and, optionally, the ghost function 1030 for outputting thedriving signal 1040.

It is noted in FIG. 10 that according to the driving signal 1040, thevibro-acoustic source element spends most of the time (e.g., 10 s of thetotal 15 s sweep time) producing low frequencies (e.g., lower than 5Hz). If the ghost function effects 1030 are not taken into account, thedriving signal for the specific vibro-acoustic source element used inthese calculations is as shown in FIG. 11. In other words, according toan exemplary embodiment, the driving signal shown in FIG. 11 takes intoconsideration the constraints 1010 on the vibro-acoustic source elementand the ESD target shape 1020, but not the ghost function effects 1030.This is an alternative operating mode of the vibro-acoustic sourceelement.

To better understand the difference between the driving signal withoutthe ghost function, i.e., the free-field, and the driving signal withthe ghost function, FIG. 12 shows the far-field sound pressure signatureat 1 m for the free-field and FIG. 13 shows the far-field sound pressuresignature at 1 m for the case with ghost.

It is noted that the above discussion about the driving signal is validfor both a vibro-acoustic source element and an array of vibro-acousticsource elements, i.e., a marine source array. If a marine source arrayis considered, then the arrangement of the vibro-acoustic sourceelements needs to be considered, and a driving signal for the wholesource array may be determined as noted above. However, because of thedifferent distances between the vibro-acoustic source elements of themarine source array, various time delays may be calculated and appliedto the elements making up the marine source array.

According to an exemplary embodiment illustrated in FIG. 14, there is amethod for determining the driving signal of a vibro-acoustic sourceelement that is configured to generate acoustic waves in water. Themethod includes a step 1400 of estimating at least one physicalconstraint 1010 of the vibro-acoustic source element; a step 1402 ofmodeling a ghost function 1030 determined by a surface of the water; astep 1404 of setting a target energy spectrum density 1020 to be emittedby the vibro-acoustic source element during the driving signal; and astep 1406 of determining the driving signal 1040 in a controller 1000based on at least one physical constraint 1010, the ghost function 1030,and the target energy spectrum density 1020.

According to another exemplary embodiment illustrated in FIG. 15, thereis another method for determining the driving signal of a vibro-acousticsource element that is configured to generate acoustic waves in water.The method includes a step 1500 of estimating at least one physicalconstraint 1010 of the vibro-acoustic source element; a step 1502 ofsetting a target energy spectrum density 1020 to be emitted by thevibro-acoustic source element during the driving signal; and a step 1504of determining the driving signal 1040 in a controller 1000 based on atleast one physical constraint 1010, and the target energy spectrumdensity 1020.

According to one or more of the exemplary embodiments discussed above,the instantaneous frequency law is matched according to the targetedenergy spectrum density based on physical limits of the vibro-acousticsource element and its depth. Further, regarding the constraint of theghost function, tuning can be obtained for the on-axis far-fieldsignature but also for any off-axis response (e.g., helpful for phasedarray application). Furthermore, the process described above permitssufficient spectral energy density in the low-frequency-end band. It isknown that the low frequency may permit evaluation of the earth'ssubsurface at deeper levels.

An example of a representative control system capable of carrying outoperations in accordance with the exemplary embodiments discussed aboveis illustrated in FIG. 16. Hardware, firmware, software or a combinationthereof may be used to perform the various steps and operationsdescribed herein.

The exemplary control system 1600 suitable for performing the activitiesdescribed in the exemplary embodiments may include server 1601. Such aserver 1601 may include a central processor unit (CPU) 1602 coupled to arandom access memory (RAM) 1604 and to a read-only memory (ROM) 1606.The ROM 1606 may also be other types of storage media to store programs,such as programmable ROM (PROM), erasable PROM (EPROM), etc. Theprocessor 1602 may communicate with other internal and externalcomponents through input/output (I/O) circuitry 1608 and bussing 1610,to provide control signals and the like. For example, the processor 1602may communicate with the sensors, electro-magnetic actuator system,and/or the pneumatic mechanism. The processor 1602 carries out a varietyof functions as is known in the art, as dictated by software and/orfirmware instructions.

The server 1601 may also include one or more data storage devices,including hard and floppy disk drives 1612, CD-ROM drives 1614, andother hardware capable of reading and/or storing information such as aDVD, etc. In one embodiment, software for carrying out the abovediscussed steps may be stored and distributed on a CD-ROM 1616, diskette1618, or other form of media capable of portably storing information.These storage media may be inserted into, and read by, devices such asthe CD-ROM drive 1614, the disk drive 1612, etc. The server 1601 may becoupled to a display 1620, which may be any type of known display orpresentation screen, such as LCD displays, plasma displays, cathode raytubes (CRTs), etc. A user input interface 1622 is provided, includingone or more user interface mechanisms such as a mouse, keyboard,microphone, touch pad, touch screen, voice-recognition system, etc.

The server 1601 may be coupled to other computing devices, such as theequipment of a vessel, via a network. The server may be part of a largernetwork configuration as in a global area network (GAN) such as theInternet 1628, which allows ultimate connection to the various landlineand/or mobile client/watcher devices.

As also will be appreciated by one skilled in the art, the exemplaryembodiments may be embodied in a wireless communication device, atelecommunication network, as a method or in a computer program product.Accordingly, the exemplary embodiments may take the form of an entirelyhardware embodiment or an embodiment combining hardware and softwareaspects. Further, the exemplary embodiments may take the form of acomputer program product stored on a computer-readable storage mediumhaving computer-readable instructions embodied in the medium. Anysuitable computer-readable medium may be utilized, including hard disks,CD-ROMs, digital versatile discs (DVDs), optical storage devices, ormagnetic storage devices such a floppy disk or magnetic tape. Othernon-limiting examples of computer-readable media include flash-typememories or other known types of memories.

The disclosed exemplary embodiments provide a source array, computersoftware, and a method for generating a driving signal for marinevibrational sources. It should be understood that this description isnot intended to limit the invention. On the contrary, the exemplaryembodiments are intended to cover alternatives, modifications, andequivalents, which are included in the spirit and scope of the inventionas defined by the appended claims. Further, in the detailed descriptionof the exemplary embodiments, numerous specific details are set forth toprovide a comprehensive understanding of the claimed invention. However,one skilled in the art would understand that various embodiments may bepracticed without such specific details.

Although the features and elements of the present exemplary embodimentsare described in the embodiments in particular combinations, eachfeature or element can be used alone, without the other features andelements of the embodiments, or in various combinations with or withoutother features and elements disclosed herein.

This written description uses examples of the subject matter disclosedto enable any person skilled in the art to practice the same, includingmaking and using any devices or systems and performing any incorporatedmethods. The patentable scope of the subject matter is defined by theclaims, and may include other examples that occur to those skilled inthe art. Such other examples are intended to be within the scope of theclaims.

What is claimed is:
 1. A method for determining a driving signal of avibro-acoustic source element that is configured to generate acousticwaves in water, the method comprising: estimating at least one physicalconstraint of the vibro-acoustic source element; modeling a ghostfunction determined by a surface of the water; setting a target energyspectrum density to be emitted by the vibro-acoustic source elementduring the driving signal; and determining the driving signal in acontroller based on the at least one physical constraint, the ghostfunction, and the target energy spectrum density.
 2. The method of claim1, wherein the vibro-acoustic source element has an electro-magneticactuator configured to actuate a piston.
 3. The method of claim 2,wherein the at least one physical constraint includes a combination ofone or more of a maximum displacement of the piston, a maximum speed ofthe piston, a maximum current of a driving mechanism that drives theelectro-magnetic actuator, and a maximum voltage of the drivingmechanism.
 4. The method of claim 2, wherein the at least one physicalconstraint includes a maximum displacement of the piston, a maximumspeed of the piston, a maximum current of a driving mechanism thatdrives the electro-magnetic actuator, and a maximum voltage of thedriving mechanism.
 5. The method of claim 4, further comprising:determining a domain of operation of the vibro-acoustic source elementas an intersection of the maximum displacement, the maximum speed, themaximum current and the maximum voltage curves.
 6. The method of claim1, wherein the ghost function takes into account a reflection of a wavefrom the surface of the water.
 7. The method of claim 1, wherein thetarget energy spectrum density is flat.
 8. The method of claim 1,wherein a majority of time corresponding to the driving signalcorresponds to a low frequency range.
 9. A controller configured todetermine a driving signal of a vibro-acoustic source element that isconfigured to generate acoustic waves in water, the controllercomprising: a processor configured to, estimate at least one physicalconstraint of the vibro-acoustic source element; receive a ghostfunction determined by a surface of the water; receive a target energyspectrum density to be emitted by the vibro-acoustic source elementduring the driving signal; and calculate the driving signal based on theat least one physical constraint, the ghost function, and the targetenergy spectrum density.
 10. The controller of claim 9, wherein the atleast one physical constraint includes a combination of one or more of amaximum displacement of a piston of the vibro-acoustic source element, amaximum speed of the piston, a maximum current of a driving mechanismthat drives the electro-magnetic actuator, and a maximum voltage of thedriving mechanism.
 11. The controller of claim 9, wherein the at leastone physical constraint includes a maximum displacement of a piston ofthe vibro-acoustic source element, a maximum speed of the piston, amaximum current of a driving mechanism that drives the electro-magneticactuator, and a maximum voltage of the driving mechanism.
 12. Thecontroller of claim 11, further comprising: determining a domain ofoperation of the vibro-acoustic source element as an intersection of themaximum displacement, the maximum speed, the maximum current and themaximum voltage curves.
 13. The controller of claim 9, wherein the ghostfunction takes into account a reflection of a wave from the surface ofthe water.
 14. The controller of claim 9, wherein the target energyspectrum density is flat.
 15. The controller of claim 9, wherein amajority of time corresponding to the driving signal corresponds to alow frequency range.
 16. A seismic survey system comprising: at leastone vibro-acoustic source element configured to generate acoustic wavesby moving a piston with an electro-magnetic actuator; a drivingmechanism connected to the electro-magnetic actuator and configured todrive the electro-magnetic actuator to generate the acoustic waves; anda controller configured to generate a driving signal for the drivingmechanism for generating acoustic waves in water, wherein the controlleris configured to estimate at least one physical constraint of thevibro-acoustic source element; receive a ghost function determined by asurface of the water; receive a target energy spectrum density to beemitted by the vibro-acoustic source element during the driving signal;and calculate the driving signal based on the at least one physicalconstraint, the ghost function, and the target energy spectrum density.17. The system of claim 16, wherein the at least one physical constraintincludes a combination of one or more of a maximum displacement of apiston of the vibro-acoustic source element, a maximum speed of thepiston, a maximum current of a driving mechanism that drives theelectro-magnetic actuator, and a maximum voltage of the drivingmechanism.
 18. A computer readable medium including computer executableinstructions, wherein the instructions, when executed, implement amethod for determining a driving signal of a vibro-acoustic sourceelement that is configured to generate acoustic waves in water, themethod comprising: estimating at least one physical constraint of thevibro-acoustic source element; modeling a ghost function determined by asurface of the water; setting a target energy spectrum density to beemitted by the vibro-acoustic source element during the driving signal;and determining the driving signal in a controller based on the at leastone physical constraint, the ghost function, and the target energyspectrum density.
 19. A method for determining a driving signal of avibro-acoustic source element that is configured to generate acousticwaves in water, the method comprising: estimating at least one physicalconstraint of the vibro-acoustic source element; setting a target energyspectrum density to be emitted by the vibro-acoustic source elementduring the driving signal; and determining the driving signal in acontroller based on the at least one physical constraint, and the targetenergy spectrum density.
 20. A seismic survey system comprising: atleast one vibro-acoustic source element configured to generate acousticwaves by moving a piston with an actuator; a driving mechanism connectedto the actuator and configured to drive the actuator to generate theacoustic waves; and a controller configured to generate a driving signalfor the driving mechanism for generating the acoustic waves in water,wherein the controller is configured to estimate at least one physicalconstraint of the vibro-acoustic source element; receive a target energyspectrum density to be emitted by the vibro-acoustic source elementduring the driving signal; and calculate the driving signal based on theat least one physical constraint, and the target energy spectrumdensity.